{
  "abstract": "We study reaction-diffusion equations with finite signed measure delays and nonlinear, possibly nonlocal feedback. We treat abstract reactions that are Lipschitz on bounded $L^2$-balls with quadratic coercivity, and pointwise cubic polynomials with positive leading coefficient in spatial dimensions at most three. For affine-growth feedback and time-independent forcing in $H^{-1}(Ω)$, both classes generate global weak solution semiflows on $X=C([-r,0];L^2(Ω))$. Besides total-variation Lipschitz stability, we obtain quantitative weak-star stability with modulus $\\varpi(d)=d\\log(e+d^{-1})$ for the abstract class and $\\varpi(d)^{1/2}$ for cubic reactions, where $d$ is the bounded-Lipschitz distance between delay measures. The estimates are uniform on bounded sets of continuous histories and yield concentration and atomic-quadrature rates. A damping condition gives common compact absorption for the abstract class. Cubic coercivity removes that smallness condition on every fixed total-variation-bounded kernel class. In both cases the global attractors are upper semicontinuous in $X$ and in $C([-r,0];H_0^1(Ω))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04195",
  "author_total": 1,
  "authors": [
    {
      "name": "Lennon Shikhman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rcdptktqwpnx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04195",
  "fulltext_url": null,
  "id": "2rcdptktqwpnx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04195",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7163569434",
  "pdf_url": "https://arxiv.org/pdf/2606.04195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rcdptktqwpnx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.04195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Kernel-Robust Dynamics for Reaction-Diffusion Equations with Measure-Valued Delay",
  "title_text": "Kernel-Robust Dynamics for Reaction-Diffusion Equations with Measure-Valued Delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/2rcdptktqwpnx",
  "venue": "arXiv",
  "versions": []
}